Innovative Maze Solving with Mathematica

A typical data structures assignment involves using stacks/queues to generate/solve mazes. This is usually performed by variants of BFS or DFS. As many of my students are currently busy with this task, I thought of presenting them a number of nontraditional solutions incorporating a real world example and some advanced techniques.

There has been a series of posts on a this problem on the Wolfram blog attacking the hedge maze at the Blenheim Palace. The solutions presented started with processing the aerial image acquired from Bing Maps, and proceeded to explore a variety of techniques from standard graph theory to a twisted application of topology.

The series progressed as follows:

• aMAZEing Image Processing in Mathematica


• Navigating the Blenheim Maze


• The Battle of the Marlborough Maze at Blenheim Palace Continues


• Retreat from Blenheim

Hope you find it interesting!

Make3D: Convert your image into 3d model

Today, While I was browsing my RSS reader... I stopped when my eyes picked this title "Make3D: Turn a 2D Picture Into a 3D Model". I followed the link to be impressed by what I saw.

Make3D is a service provided by Stanford University. Make3D takes a single two-dimensional image, process it, and creates a "fly around" three-dimensional model. You can then view the three-dimensional model and feel the depths of the pixels in the image.

"The service is based on an algorithm created by Stanford students Andrew Ng, Ashutosh Saxena and Min Sun that won the best paper award at the 3D recognition and reconstruction workshop at the International Conference on Computer Vision in Rio de Janeiro in October 2007." [Make3D: Turn a 2D Picture Into a 3D Model, accessed on: Feb 27, 2008]

Make3D uses powerful machine learning techniques, to learn the relation between small image patches and their depth and orientation. This allows it to model 3-d structures such as slopes of mountains or branches of trees. [Make3D home page, accessed on Feb 27, 2008]

I created and account and gave it a try. Result of my trial doesn't look so good but they have other models in the Gallery which look so good. Here is my try:
I uploaded this...

and I got this 3D model...

Just follow this link to Make3D home page, and you will find other links to the information you may need. You can view their publications in this area of 3D image construction; You can download their code; You can navigate to the FAQ for how it works and other questions; You can browse their Gallery; You can create an account and upload your images to get their 3D model; ...etc

Before I end this post, I would like to highlight that one of the graduation projects this year in class 2008, Computer and Systems Engineering Department, Alexandria University is working in this area -3D image construction- let's hope them the best of luck and wish we can see something impressive by the end of this semester.